I suppose you're referring to a Riemann sum.

Using the right endpoint method,

Since a=0, we have

Sub into what is to be integrated:

The thing to do here is to write the sum in terms of n.

The sum of the first n fourth powers is given by:

So, you get:

Expand out and take the limit as

You should get your answer the same as if you integrated the 'quick' way.